Answer on Algebra Question for Whitney

2010-07-13T04:59:49-0400

Question #451

With what accuracy should the length of the equator be measured to figure out the volume of the Earth with the accuracy of 1 km&sup3; (If consider the Earth as the ideal sphere with the radius of 64000 km)?

Expert's answer

2010-07-13T05:04:41-0400

Let r be the radius of the Earth. Then the length of the equator is L = 2&pi;r. And the volume is V = (4/3)*&pi;r&sup3;. Thus, we can define the volume through the length of the equator as V = L&sup3;/6&pi;&sup2;. Thus, if we need to measure this value with the accuracy of 1 km&sup3; we should measure L with the accuracy of &radic;3(6&pi;&sup2;)km.

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